The cohomological rigidity property, considered as above, was initially studied by Kempf [1]} and Luk and Yau [2]} by using different approaches. A commutative algebra interpretation of the cohomological rigidity property has been examined by Huneke and Wiegand [3]}. More precisely, given a reflexive module \(M\)  over a hypersurface ring \(R\) , Huneke and Wiegand determined new criteria for the freeness of the module \(M\)  in terms of the vanishing of \(\operatorname{H}^i_{\mathfrak {m}}(M\otimes _RM^*)\)  for some \(i\) . Furthermore, Huneke and Wiegand generalized the aforementioned result of Luk and Yau via the machinery of commutative algebra.
